Geodesic
Elliptic problems with radiation conditions on edges of the~boundary
Sbornik. Mathematics, Tome 77 (1994) no. 1, pp. 149-176

Voir la notice de l'article provenant de la source Math-Net.Ru

A study is made of formulations of elliptic boundary value problems connected with the addition of radiation conditions on edges of the piecewise smooth boundary $\partial G$ of a domain $G\subset\mathbb{R}^n$. Such formulations lead to Fredholm operators acting in suitable function spaces with weighted norms. The basic means of description is the generalized Green formula, which contains in addition to the usual boundary integrals also integrals over an edge $M$ of bilinear expressions formed by the coefficients of the asymptotics of the solutions near $M$. Thus, the edge and the $(n-1)$-dimensional smooth part of the boundary are on the same footing-both $M$ and $\partial G\setminus M$ are represented by their contributions to the generalized Green formula. This permits the construction of a theory of elliptic problems in which the generalized Green formula takes the role of the usual Green formula in the smooth situation. 
@article{SM_1994_77_1_a9,
     author = {S. A. Nazarov and B. A. Plamenevskii},
     title = {Elliptic problems with radiation conditions on edges of the~boundary},
     journal = {Sbornik. Mathematics},
     pages = {149--176},
     publisher = {mathdoc},
     volume = {77},
     number = {1},
     year = {1994},
     language = {en},
     url = {http://geodesic.mathdoc.fr/item/SM_1994_77_1_a9/}
}
TY  - JOUR
AU  - S. A. Nazarov
AU  - B. A. Plamenevskii
TI  - Elliptic problems with radiation conditions on edges of the~boundary
JO  - Sbornik. Mathematics
PY  - 1994
SP  - 149
EP  - 176
VL  - 77
IS  - 1
PB  - mathdoc
UR  - http://geodesic.mathdoc.fr/item/SM_1994_77_1_a9/
LA  - en
ID  - SM_1994_77_1_a9
ER  - 
%0 Journal Article
%A S. A. Nazarov
%A B. A. Plamenevskii
%T Elliptic problems with radiation conditions on edges of the~boundary
%J Sbornik. Mathematics
%D 1994
%P 149-176
%V 77
%N 1
%I mathdoc
%U http://geodesic.mathdoc.fr/item/SM_1994_77_1_a9/
%G en
%F SM_1994_77_1_a9
S. A. Nazarov; B. A. Plamenevskii. Elliptic problems with radiation conditions on edges of the~boundary. Sbornik. Mathematics, Tome 77 (1994) no. 1, pp. 149-176. http://geodesic.mathdoc.fr/item/SM_1994_77_1_a9/